The Franklin Elementary Algebra

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1882 Excerpt: ... wrought in Art. 228. Had the signs of the co-efficients of y, the quantity to be eliminated, been unlike, the elimination would have been ...
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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1882 Excerpt: ... wrought in Art. 228. Had the signs of the co-efficients of y, the quantity to be eliminated, been unlike, the elimination would have been effected by addition instead of subtraction. The following examples will further illustrate this method. Illustrative Examples. I. Given 7 x--Sy = 9 and 4x + by = 32. to find the values of r and y. Multiply both members of (1) (1) 7x--3y= 0 by 5, and of (2) by 3, and mlil (2) 4x + 5y = 32 the results (3) and (4) to get (5). (3) 35 x--15 # = 15 Note. For the sake of brevity we (4) 12i+15y = 96 sj1eak of adding or subtracting one (5) 47 x = 141 equation to or from another; but the x = 3 meaning is that each member of one equation is added to or subtracted from the corresponding member of the other. 21-3 y = 9 Substitute 3 for x in (1), and-3y =-12 find the value of y. y=4. Verify by substituting 3 for r and 4 for y in (2). 12 + 20 = 32. If we had chosen to eliminate x, the work would have been as follows: (3') 28x-12y = 36 Multiply both members of (1) (4') 28 x + 35 y = 224 by 4, and of (2) by 7, and sub-(5') 47=188 tract the first result (3') from the y = 4 second (4'). 7x-12 = 9 Substitute 4 for y in (1), and 7x=21 find the value of x. x = 3. II. Given =-and----z = 7, to find x and y. V 3 y+1 4 Equations (1) and (2) cleared... x+ 1_1 of fractions give (3) and (4). y 3 By subtracting 3 and y from each . x _ 1 member of (3), and y from each y + 1 4 member of (4), the equations are (3) 3x + 3 = y further reduced to the forms (5) ($ 4x=y+l and (6). Then y is eliminated by, -. q._, .__a subtracting (5) from (6). The. ..-j value of y is found from (3)...-. Before eliminating by addi 12-4-3--' tion or subtraction, equations should always be reduced to V--simple forms like (5) and (6). 234. From the forego...
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